A conducting sphere of radius `10 cm` is charged `10 muC`. Another uncharged sphere of radius `20 cm` is allowed to touch it for some time. After that if the spheres are separated, then surface density of charges, on the spheres will be in the ratio of

Options

A. `1:4`
B. `1:3`
C. `2:1`
D. `1:1`

Answer

C

Explanation

After redistribution new charges on sphere are
`Q'_(1)= ((10)/(10+20))xx10=(10)/(3)muC`
and `Q'_(2)=((20)/(10+20))xx(20)/(3)muC`
Ratio of charge densities `(sigma_(1))/(sigma_(2))=(Q'_(1))/(Q'_(2))xx(r_(2)^(2))/(r_(1)^(2))`
`=(10//3)/(20//3)xx((20)/(10))^(2)=(2)/(1) {sigma=(Q)/(4pir^(2))}`